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Abstract
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid.
Keywords
feedback, controllability, flow control, hydrodynamics, nonlinear control systems, two-phase flow, geometric control, particle manipulation, cyclic fluid boundary excitations, controlled cyclic motion, circular rigid body, 2D perfect fluid, control system, nonlinear controllability, feedback-based gait, Stokes fluid

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Citation

Please use this url to cite or link to this publication:

Chicago
Or, Yizhar, Joris Vankerschaver, Scott D Kelly, Richard M Murray, and Jerrold E Marsden. 2009. “Geometric Control of Particle Manipulation in a Two-dimensional Fluid.” In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009), 19–26. Piscataway, NJ, USA: IEEE.
APA
Or, Y., Vankerschaver, J., Kelly, S. D., Murray, R. M., & Marsden, J. E. (2009). Geometric control of particle manipulation in a two-dimensional fluid. 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009) (pp. 19–26). Presented at the 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009), Piscataway, NJ, USA: IEEE.
Vancouver
1.
Or Y, Vankerschaver J, Kelly SD, Murray RM, Marsden JE. Geometric control of particle manipulation in a two-dimensional fluid. 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009). Piscataway, NJ, USA: IEEE; 2009. p. 19–26.
MLA
Or, Yizhar, Joris Vankerschaver, Scott D Kelly, et al. “Geometric Control of Particle Manipulation in a Two-dimensional Fluid.” 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009). Piscataway, NJ, USA: IEEE, 2009. 19–26. Print.
@inproceedings{1073593,
  abstract     = {Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid.},
  author       = {Or, Yizhar and Vankerschaver, Joris and Kelly, Scott D and Murray, Richard M and Marsden, Jerrold E},
  booktitle    = {2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009)},
  isbn         = {9781424438716},
  keyword      = {feedback,controllability,flow control,hydrodynamics,nonlinear control systems,two-phase flow,geometric control,particle manipulation,cyclic fluid boundary excitations,controlled cyclic motion,circular rigid body,2D perfect fluid,control system,nonlinear controllability,feedback-based gait,Stokes fluid},
  language     = {eng},
  location     = {Shanghai, PR China},
  pages        = {19--26},
  publisher    = {IEEE},
  title        = {Geometric control of particle manipulation in a two-dimensional fluid},
  url          = {http://dx.doi.org/10.1109/CDC.2009.5399499},
  year         = {2009},
}

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